8 Answers
8

The player problem that rules changes seem to handle really well is boredom. If combat drags on and on, or if you have two players who are really interested in setting up elaborate tactics on the battemap and one who just wants to roll the dice and move on, then changing the rules to better suit the group as a whole can help.

Another thing rules can have a real impact on is if the group is falling into a behavior that no one actually enjoys. For instance, if people are getting distracted with side conversations, but everyone in the group agrees that they'd rather have a more immersive experience, then "IC talk only" can make sense. If no one at the table is actually enjoying the elaborate battlemap tactics, then changing to a system where those tactics are less important can help.

Most of the examples you cite, on the other hand, are most likely better handled by frank discussion and perhaps changing the composition of the group than by trying to fix it with rules.

In some rare cases, rules tweaks can bring borderline cases back to participation. For example, streamlining combat or task systems can take a game that has an issue and make it more playable.

But in general, problems with individuals tend to be deeper than rules; setting is often far more important to individual players than the rules.

Going through your examples:

Someone is not really interested in the game, and reads and ignores play until they have to roll.

Rules tweaks to the current game probably won't help this one. A change of game, character or setting might, but don't count on it. Flat out ask them why they play; pay attention. If they are not there for the game, then perhaps it's time for them to find something else to do.

The GM favors certain players over others

Again, rules tweaks won't help, but certain mechanics are capable of reducing it. Problem is getting the GM to play those games. Burning Empires has a scene budget mechanic that gives every player equal numbers of scenes, and the players focus the scenes themselves, so the GM just sets action difficulties.

Two players have an out-of-game disagreement and it is showing up in the game.

A set of table rules might affect this, but it's beyond the scope of the game itself. Simply put, humans don't isolate stuff well, and it is bound to leak through, but it's also not something where the game itself will help.

Switching to a PVP system (such as Houses of the Blooded) will actually tend to exacerbate such behaviors.

Talking to them about it might help, however, and will at least have the potential to get it moving towards resolution. It could also result in a nasty blowup, argument, and storm out.

Players make last-minute cancellations or can't prioritize a regular game time.

An in-game penalty for no-call or late-call no-show can reduce that, but it also can be a stressor that breaks a group.

Players are real people with real life. If someone's in an on-call job, accepting them into the group includes accepting that they may be called out just before or even during session. If someone's blowing you off for a good book, odds are the game isn't why they're playing.

Some players just never get into it as a hobby, seeing it merely as a way of passing some time. Just give them characters easily written in and out of the ongoing story... A deranged vapire with MPD comes to mind from one friend's Werewolf campaign...

The GM can't tolerate deviations from the story.

Again, no rules tweak will solve this. This is simply someone who probably shouldn't be GMing. The story should emerge from play, not follow some arbitrary script the GM has thought up.

It's fine to have boundaries, especially if everyone has agreed it's time to use a module or specific adventure. But in more sandbox-style campaigns, no, this is bad GMing. And I'm not generally one to claim "Badwrongfun must stop!" But in this case, it's obvious that, for you, it's not fun, and "badwrongboring" and "badwrongannoying" really make it a pain.

I don't believe that rules changes, or tweaks, can solve many interpersonal problems. Using dice to solve some issues--minor arguments over rules--can solve the problems when they arise around the table; however, it won't do much to prevent problems from reoccurring.

Instead of running an RPG at the table, I'd try running a board game or a story game to help build group cohesion. If the group doesn't click, the problems won't go away, so building trust within the group could end some of the issues.

Simple rule tweaks can sometimes help, but just with minor things. Your initial choice of game/System can help prevent some problems... no, wait, I'm saying it backwards: bad rules can and do generate problems where there would be none.
But the problems you listed in your OP are an order of magnitude larger than what rules can affect. Those are symptoms of people not being up on the same page about playing together (or about playing an RPG at all). Can only be solved by honest discussion, and should honest discussion be impossible that would signal an impossibility for those people to properly play together as well.

I don't think that mere tweaks to the rules can fix these problems. You would need to change the rules drastically. Changing the rules drastically usually means playing a different game.

If you are having these sorts of problems I highly suggest finding a game that avoids them entirely. For example, if people are being distracted or aren't involved, pick a game with a turn-taking mechanic. People will be forced to get involved whenever its their turn, and will probably be involved on other people's turns as well. Prime Time Adventures is a good example.

If the problem is the GM, then try to play a game that doesn't even have a GM at all. At a minimum you could play a game like Inspectres where the line between GM and player is clearly drawn, so there can't possibly be any arguing or favoring.

If players are arguing with each other in-game, and you can't settle those arguments, then perhaps you should play a game that has an argument resolution mechanic. In most tabletop games players can argue whether the party should day door number one or door number 2 until they are blue in the face. In a game like Burning Wheel you would have a duel of wits, and the dice would decide. Not only does it solve the problem, but it's really satisfying.

As for players who bring their out of game drama into the game, or can't show up regularly, I don't think changing games can fix those problems. The best you can do is confront them on the issue, and then just drop them from your game if they aren't compatible with your group. You can't let the whole game suffer on account of a few bad eggs.

Someone is not really interested in the game, and reads and ignores play until they have to roll.

This is likely the fault of an initiative based combat system. Having less players is one solution, but having a system that doesn't operate by initiative ticks is another. A system like Hero that has different numbers of turns for each player, or a system like Aces & Eights that times things according to the action you're taking might lead to more involvement. Similarly, a system like HeroQuest that handles conflicts together, and gets people to all be involved in a single action, rather than waiting their turn would get around this.

The GM favors certain players over others

This depends on the specific implementation, but giving players more power, such as in Donjon or FATE would circumvent this to a degree.

Two players have an out-of-game disagreement and it is showing up in the game.

Beast Hunters specifically tries to avoid it, as it assumes a couple playing together, I'm not sure how successful it is. It ritualises entering the game, and leaving it, which may or may not help. It's also something that could be adapted to other game systems without much difficulty.

Players make last-minute cancellations or can't prioritize a regular game time.

This likely wouldn't be heavily involved in system, but a game like Smallville would probably sustain it a lot better than other systems which assume party based play instead of main characters who are probably in some degree of opposition to each other. Birthright for AD&D, and Reign's company rules, as well as Legends of Anglerre's could also address this from a mechanical standpoint. Otherwise the solution is setting based - have the setting have plausible fast travel. It'd work in modern settings where someone might be on a business trip, but medieval settings it likely wouldn't.

The GM can't tolerate deviations from the story.

I guess this depends on the system you're playing. D&D 4e rather assumes there won't be any deviations, and gives out guaranteed XP and treasure parcels. Earlier editions, particularly AD&D 2e could reward sticking to the railroad by giving out gobs of XP (and most published adventures assumed this, if you do what the designer wants, you get a ton more XP than if you do your own thing). The GUMSHOE system is also designed to make sure players get all the clues if they're at least looking somewhere, which can ensure a greater likelihood of following the path, as it ends up playing out similar to Broken Sword.